Séminaire CIMMUL | Alex Shestopaloff

Bayesian Partial Reduced-Rank Regression

Alex Shestopaloff

University of Guelph

Résumé

Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix. To address this limitation, Partial RR can be used, where the response vector and the coefficient matrix are partitioned into low- and full-rank sub-groups. However, existing methods for Partial RR assume known group structure and rank. We instead treat them as unknown parameters to be estimated and propose an approach to (1) infer the low- and full-rank group memberships from the data, and then, (2) conditionally on this allocation, estimate the corresponding (reduced) rank. Both steps are carried out in a Bayesian fashion, allowing for full uncertainty quantification.